What does two slasshes mean in a unix file system?

Here is my code:

find ./ -name Desktop -type d   
.//Desktop
find: .//Documents/Library: Permission denied

Why two slashes following the period.? What does .// mean?I thought in Unix, the file system is named after appending one slash at the END of the folder name? Hence Documents/ means the document directory.

They have no special meaning. Your find is just outputting prefix './' + path found. (try with . instead of ./, or with no path specification at all, i.e. find -name Desktop -type d!).

Under POSIX filesystems, directory//abc is the same as directory/abc.

Hence Documents/ means the document directory.

no, the directory is called "Documents" (and its full path is probably something like /home/jxhyc/Documents).

Some commands (e.g. rsync) interpret a trailing slash as "treat this differently than a normal file", but that's not Unix semantics, that's up to the individual program.